29 citations · 88 across the 15 of their papers we have counts for
16 papers
Capacitary estimates for solutions to nonlocal Dirichlet problems
Minhyun Kim, Se-Chan Lee, Marvin Weidner
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity densit…
Nonnegative solutions to nonlocal parabolic equations
Naian Liao, Marvin Weidner
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a…
Time-insensitive nonlocal parabolic Harnack estimates
Naian Liao, Marvin Weidner
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal…
The Harnack inequality fails for nonlocal kinetic equations
Moritz Kassmann, Marvin Weidner
We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoellipt…
Obstacle problems for nonlocal operators with singular kernels
Xavier Ros-Oton, Marvin Weidner
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential op…
Gradient Riesz potential estimates for a general class of measure data quasilinear systems
Iwona Chlebicka, Minhyun Kim, Marvin Weidner
We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates f…
Semiconvexity estimates for nonlinear integro-differential equations
Xavier Ros-Oton, Clara Torres-Latorre, Marvin Weidner
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with ge…
The parabolic Harnack inequality for nonlocal equations
Moritz Kassmann, Marvin Weidner
We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove t…
Nonlocal operators related to nonsymmetric forms II: Harnack inequalities
Moritz Kassmann, Marvin Weidner
Local boundedness and Harnack inequalities are studied for solutions to parabolic and elliptic integro-differential equations whose governing nonlocal operators are associated with…
Markov chain approximations for nonsymmetric processes
Marvin Weidner
The aim of this article is to prove that diffusion processes in with a drift can be approximated by suitable Markov chains on . Moreover, we inve…
Nonlocal operators related to nonsymmetric forms I: Hölder estimates
Moritz Kassmann, Marvin Weidner
The aim of this article is to develop the regularity theory for parabolic equations driven by nonlocal operators associated with nonsymmetric forms. Hölder regularity and weak Harn…
Harnack inequality for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness a…
Regularity for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of -type and for weak solutions to a related class of nonlocal equ…
Upper heat kernel estimates for nonlocal operators via Aronson's method
Moritz Kassmann, Marvin Weidner
In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to the Cauchy problem governed by a second order divergence form operator with uniformly…
The concentration-compactness principle for the nonlocal anisotropic -Laplacian of mixed order
Jamil Chaker, Minhyun Kim, Marvin Weidner
In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrabil…
Parabolic problems for direction-dependent local-nonlocal operators
Jamil Chaker, Moritz Kassmann, Marvin Weidner
We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting co…